Total Tricks question

[Fluffy]

What is the average number of total tricks for any given hand double dummy without even looking at your hand?

 

What about after looking at your shape? just a few common shapes like 4333, 4432, 5431, 5521, 7321...

[jogs]

What is the average number of total tricks for any given hand double dummy without even looking at your hand?

 

What about after looking at your shape? just a few common shapes like 4333, 4432, 5431, 5521, 7321...

 

You need more restrictions on the side conditions.

Your questions cover too much territory.

 

4333 generates fewer tricks than 4432.

5422 generates fewer tricks then 5431.

 

No one has studied and published info on this topic.

[yunling]

I reanalyzed someone else's simulation on 1,000,000 hands(sorry that I failed to find the reference) and the result is

 

Shape Expected Total Tricks

Any 16.87

4333 16.21

4432 16.41

5332 16.61

4441 16.77

5422 16.84

5431 16.99

6322 17.19

6331 17.32

5521 17.47

6421 17.57

5440 17.54

5530 17.80

7222 17.86

6430 17.88

7321 18.01

6511 18.29

6520 18.45

7411 18.47

7420 18.59

[Zelandakh]

No one has studied and published info on this topic.

I reanalyzed someone else's simulation on 1,000,000 hands(sorry that I failed to find the reference) and the result is

Glad to see that is clear then. I took the liberty of scaling the data provided by yunling by expected loss/gain and then adding in a comparison of 3 popular evaluation methods - 3/2/1 count; 5/3/1 count; Zar points; and Zar points using two simple normalisation formula for comparison [(ZP - 8)/2] and [3(ZP - 10)/5]. Please take these statistics with more than a pinch of salt since the analysis is for Total Tricks and not tricks for our side. Some of the Total Tricks will be for the other side so the true optimised values will be lower than the Opt column suggests. For evaluation purposes, estimates of our expected tricks are imho more useful.

 

Shape TTs +/- Adj+/- Opt 321 531 Zar MZP1 MZP2

4333 16.21 -0.66 0.00 0.00 0 0 08 0.0 0

4432 16.41 -0.46 0.20 0.60 1 1 10 1.0 1.2

5332 16.61 -0.26 0.40 1.20 1 1 11 1.5 1.8

4441 16.77 -0.10 0.56 1.68 2 3 11 1.5 1.8

5422 16.84 -0.03 0.63 1.89 2 2 12 2.0 2.4

5431 16.99 +0.12 0.78 2.34 2 3 13 2.5 3

6322 17.19 +0.32 0.98 2.94 2 2 13 2.5 3

6331 17.32 +0.45 1.11 3.33 2 3 14 3.0 3.6

5521 17.47 +0.60 1.26 3.78 3 4 14 3.0 3.6

5440 17.54 +0.67 1.33 3.99 3 5 14 3.0 3.6

6421 17.57 +0.70 1.36 4.08 3 4 15 3.5 4.2

5530 17.80 +0.93 1.59 4.77 3 5 15 3.5 4.2

7222 17.86 +0.99 1.65 4.95 3 3 14 3.0 3.6

6430 17.88 +1.01 1.67 5.01 3 5 16 4.0 4.8

7321 18.01 +1.14 1.80 5.40 3 4 16 4.0 4.8

6511 18.29 +1.42 2.08 6.24 4 6 16 4.0 4.8

6520 18.45 +1.58 2.24 6.72 4 6 17 4.5 5.4

7411 18.47 +1.60 2.26 6.78 4 6 17 4.5 5.4

7420 18.59 +1.72 2.38 7.14 4 6 18 5.0 6

[WellSpyder]

.... scaling the data provided by yunling by expected loss/gain ...

Should it be obvious to me what you mean here? (I'm afraid it's not.) I take it these aren't expected losses or gains in imps or something, since comparisons will be with someone holding the same shape as me....

[Zelandakh]

Sorry, not very well explained. The third column is the expected gain or loss in expected total tricks, so 16.21 - 16.87 = -0.66 for 4333. The 4th column is the same thing but adjusted so that 4333 is set to 0, which is (arguably) useful for comparing the evaluation schemes. So Col4 = Col3 + 0.66. The Opt column (column 5) is now Col4 * 3, on the basis that 3 hcp is roughly a trick. That is designed to give some basis for comparison with the evaluation methods, columns 6, 7, 9 and 10. Column 6 is 321 points; column 7 is 531 points. Column 8 is the raw Zar Points, from which columns 9 and 10 are produced using the formulae given in post #4.

[WellSpyder]

Sorry, not very well explained. The third column is the expected gain or loss in expected total tricks, so 16.21 - 16.87 = -0.66 for 4333. The 4th column is the same thing but adjusted so that 4333 is set to 0, which is (arguably) useful for comparing the evaluation schemes. So Col4 = Col3 + 0.66. The Opt column (column 5) is now Col4 * 3, on the basis that 3 hcp is roughly a trick. That is designed to give some basis for comparison with the evaluation methods, columns 6, 7, 9 and 10. Column 6 is 321 points; column 7 is 531 points. Column 8 is the raw Zar Points, from which columns 9 and 10 are produced using the formulae given in post #4.

Thanks - much clearer now, and an interesting way of looking at things. (Now all we need is a simple way to estimate how much of the increase in total tricks from extra shape actually means more tricks for you rather than the oppo... And maybe an adjustment is needed for the expected increase in partner's distributional values, too, otherwise you will be double-counting the value of this?)

[yunling]

Please take these statistics with more than a pinch of salt since the analysis is for Total Tricks and not tricks for our side. Some of the Total Tricks will be for the other side so the true optimised values will be lower than the Opt column suggests. For evaluation purposes, estimates of our expected tricks are imho more useful.

 

I don't think these data are good for hand evalution purpose. :unsure: As I know, 4441 hands behave better than 5422 in both offense and defense, though the latter has more TTs. Can't understand why most methods consider 5422 as the better hand.

[helene_t]

well if 4441 is better for both offense and for defense, then (assuming "better by the same degree") the total tricks would be the same for the two shapes.

 

But frankly I don't understand the purpose of this exercise. Total tricks estimates are usually used for bidding decisions that are made after a lot more info is available than the hand itself. In particular, if you are 5431 it may matter if the suit bid by opps is your singleton or your 3-card suit.

 

So what's the point of this exercise? Maybe it could be used to assess the lawfullness of various presumed fit openings. But the lawfullness of an opening depends on whether we can find an existing fit and, if so, at which level. If I open a Muiderberg with some 5431-shape then the expected total tricks for a 5431-shape will tell me somthing about how lawfull it is, but really I need to know:

- the weighted average TT across all the muiderberg shapes, not only 5431

- the TT based on the fit that we will actually find which will sometimes be the second best fit

- whether we can find the fit at the 2-level or not (obviously if it is in the opening suit we can)

- the chance of getting to a contract which is not lawfull but still better than par as long as it isn't doubled (and, given that, the chance of getting away with it)

- the chance of having values for 3NT which obviously doesn't require a certain number of TTs to be lawful.

[jogs]

I don't think these data are good for hand evalution purpose. :unsure: As I know, 4441 hands behave better than 5422 in both offense and defense, though the latter has more TTs. Can't understand why most methods consider 5422 as the better hand.

 

But you have 5422 as the better hand.

 

4441 16.77

5422 16.84

 

What's the variance or std dev. of your estimates?

[Zelandakh]

Absolutely, and I think your reasoning is one reason why the TT approach is fatally flawed in practise. It is simpler, and probably more accurate, just to look at a huge number of real hands and to calculate from that the distrubtional effects of pairs of shapes. From there it is a small step to evaluating the individual shapes.

 

A long time ago, back when ZPs were new, I seem to recall a major project being done to achieve something along these lines with the emphasis on game level hands. My recollection was that ZPs performed very well but that 531 points were a fraction better. The analysis also suggested that evaluation methods based on 321 honour points (including ZP 6421 and 4.5/3/1.5/1) were considerably better than traditional Milton. I do not know whether the results were robust but I can certainly believe that ZP and 531 points were more accurate than most alternatives and fairly close together. I wish I had time and energy enough to do something like this myself but I doubt that is going to happen anytime soon.

 

I suspect that ZPs are actually better than 531 in terms of ranking the hand types in order but something does not seem to work properly with the scaling. It would not surprise me at all if there is a way of adjusting ZPs that would work better than either scheme alone and be compatible with 4.5/3/1.5/1 count honour points. If the end result was simple enough, that would be a breakthrough that could help club players greatly. Of course, creating a scheme that could work as a knowledge-based system is never going to be practical for human players - it would be far too complicated to be useful. On the other hand, such an idea would be beneficial to robot-builders, in much the same way as the GM-level evaluation of positional aspects of chess revolutionised computer engine design.

 

Basically I see two goals for evaluation. One is to create the most accurate evaluation scheme that uses simple numbers that almost any club player could use quickly. The second is to create an optimised evaluation model that takes into account every piece of known information, either for use in computers or for providing pointers to advanced players on where they can fine-tune their simple evaluations. I think most of the stuff posted about evaluation that do not move towards one of these two models is simply pointless and without any practical value. Therefore it is always in my mind to find ways of comparing eveluation models by normalising them to the same comparative levels. That makes it easier to judge whether we are moving in the right direction, even when two evaluation schemes appear at first glance to be completely incomparable (MLTC is a good example).

[aguahombre]

Like Helene, I don't think the original conditions of this excercise serve any real purpose.

 

I do question the hollow "knowledge" that 4-4-4-1 pattern bodes well for both offense and defense. Without needing much mathematical prowess, we can see that if we are the ones holding the 4-4-4-1 hand, it will be better for defense than more balanced distributions. Every 8- or 9-card fit the opponents might have will break unfavorably. But, for offense, we have found this particular array to be awkward in both bidding and declarer play opposite whatever partner has.

 

I would certainly welcome some mathematical analysis which shows 4-4-4-1 is good a priori for offense, and thus my personal experience is atypical.

[jogs]

I thought DD analysis was slow and painful. How many iterations can the computer perform in a minute?

[yunling]

But you have 5422 as the better hand.

 

No, more TTs don't mean it is a better hand. When you have 5422, more tricks will belong to opponents.

[TylerE]

I thought DD analysis was slow and painful. How many iterations can the computer perform in a minute?

 

Double dummy isn't bad with modern techniques, especially on multi-core processors. Dozens of hands a second isn't unreasonable. What is much slower is single dummy play ala GIB or Jack.

[jogs]

Double dummy isn't bad with modern techniques, especially on multi-core processors. Dozens of hands a second isn't unreasonable. What is much slower is single dummy play ala GIB or Jack.

 

12 X 3600 seconds/hour = 43,200

 

Round it up to 50,000.

 

That is still 20 hours for 1,000,000 iterations.

 

Sometimes DD gives a different number of tricks depending on which partner declares.

Some boards have two 4-4 fits. Some boards have a 4-4 and a 5-3 fit.

On rare occasions on the slam level the 4-4 fit makes one more trick

than the 5-4 fit.

[blackshoe]

On rare occasions on the slam level the 4-4 fit makes one more trick

than the 5-4 fit.

Interesting. How rare? Reason I ask is that I read somewhere a recommendation to always play your slam in the 4-4 fit if you can.

 

What happens at the game level?

[gordontd]

Interesting. How rare? Reason I ask is that I read somewhere a recommendation to always play your slam in the 4-4 fit if you can.

 

What happens at the game level?

I suspect it's more common at the slam level than at the game level. Certainly, if you try to construct teaching hands to illustrate the point, it always seems easier to come up with slam hands than game hands.

[aguahombre]

Profoundly expressing the obvious: The slam level is always 12+ tricks, whether in NT or in suit, but the game level is only three in NT --but 4 or 5 in suit. So, the considerations are different.

[blackshoe]

What does NT have to do with whether you play in a suit with a 4-4 fit or a suit with a 5-3 fit?

 

I think that at the game level you'd be looking at whether to play in 4♥ or 4♠ or possibly whether to play in 5♣ or 5♦. Other combinations are probably irrelevant. Maybe 4-4 in a major and 5-3 in a minor, but I don't think most people are going to figure that out - if they find the major fit, they'll play in it, even if it doesn't make and the minor fit does (at game level).

 

The one really significant difference between game level and slam level, other than number of tricks, is that you have less room to find the double fit (particularly when it's in the majors) when you need to stop at the game level. So it seems to me, anyway.

 

OTOH, if "everybody" is in the 5-3 just making (either game or slam, whatever the suit), then the overtrick in the 4-4 will get you a top. at MPs. At IMPs 1 overtrick is not usually a consideration.

[mycroft]

Frequently the extra trick is the "unavoidable loser" you have when you're Ax opposite xx (or 3v3 or whatever) that you can pitch on the long card in the 5-4 after pulling trumps, and then ruff with the "fifth" trump (this tends to only work when they break 3-2). So you make 4-and-a-ruff, and 5, and the A, and enough else to make 12 tricks; whereas in the 5-4 fit, you have nowhere to pitch the loser, and you make 5-and-no-ruff, and 4, and the A, and only enough for 11.

 

(if your loser is in the 5-4 suit, then this works if they don't lead the scary suit, or...)

 

In slam, this is quite likely because you expect to have control of both suits. In game, you're less likely to have control of both suits, and that gives the opps enough time to develop and take that "unavoidable loser" before you develop and take your pitch. Frequently the 5-4 fit works better, because bad breaks or multiple losers are less likely, less damaging, and easier to control than in the 4-4 fit (even 5-3 can be more tolerant of bad breaks than 4-4).

[blackshoe]

Hm. Good point, Mycroft.